Hurricane Douglas is supposed to reach my island (Oahu) by tomorrow. So before I swirl In the vortex I thought I’d share this article I read by Haug. 2020 is the year of the oddity. We as a collective, have seen a lot of power laws at work. Kobe dying (RIP), a pandemic shutting down the economy, market “crash”, negative crude oil, etc etc, the negative crude prices shocked us all, and I think this should be looked at more. We all know stock prices can’t go negative, this is why lognormality is present. But maybe stocks can go negative? forget stocks for a minute, let’s look at options. Playing with Black Scholes inputs, let’s big thumb the vol input and enter a negative number. Option premium cannot be negative, right? Well, inputting negative volatility for a call option, then multiplying the result by negative one actually gave me the value of a put, and vice versa. This idea came from Haug btw! So he dug deeper and started studying about Einstein’s relativity, symmetry, and space time, in relations to matter and anti matter. “In 1889, the physicist Arthur Schuster wrote a letter to the journal “Nature”, stating the question “If there is negative electricity, then why not negative gold as yellow as our own?”.” Basically Haug applied this negativity (matter/antimatter) to volatility variables. Basically this was formulated into what’s called put-call duality. c(S,X,T,r,b,σ)= p(−S,−X,T,r,b,−σ) Haug states: “In the option world we get the similar rule A matter-call (right-handed derivative instrument) is symmetrical with an antimatterput (left-handed derivative instrument), and vice versa. The product stems from the fact that the results for both puts and calls can be obtained if one introduces a polarity variable, for example either +1or−1. The polarity variables enter through the boundary conditions and are thus present in the solution. At least this is part of the story. Not only does this result hold for the option value, but naturally also for all the option Greeks: delta, theta, rho, etc. For example the delta of a call will equal the antimatter-delta of a put. The matter/antimatter-option rule is not only stimulating for the imaginary brain cells, but the result is actually very robust and simplifies coding and implementation of many derivatives models. You need only the formula and code for a call or for a put, as one can easily be translated into the other using an antimatter-mirror. As Dr Carr the symmetry Wizard pointed out to me, the result only holds when the pricing formulas involve σ times √T, rather than √σ2T . The result can easily be extended to several exotic options, like barriers and Asian options. In the financial markets, empirical research suggests that most assets and commodities have leptokurtic distributions (fat-tails and peaked top). We can use option models to describe the distribution by using higher order moments like skewness and kurtosis.” anywho, there’s a lot more to this, but I thought I’d share this esotericism of mathematical finance with y’all, maybe get a discussion going on antimatter calls and puts.
Btw If you’d like to read this article, it’s titled, “A Look In The Antimatter Mirror” in Haugs great book “Derivatives Models on Models”
Also, there's no such thing as "negative" electricity. You have a source of electrons and a sink for them; "positive" and "negative" are just convenient (and unfortunately misleading as well as incorrect) labels.
Physical oil went negative as well, in fact some contracts where there before WTI. Really, there was nothing surprising about it. If you have a product that requires storage, you gonna get charged to store it. If the consumption rate is lower than the production rate, it’s gonna go negative. There was a fantastic sci-fi short story about it years ago, art fully predicted life.
I am on the north shore of Maui - this was the disaster from the last hurricane, let's hope this one is not to bad.